Triangle Inequality and bounds

I need help answering the following question:

Use triangle Inequality and reverse triangle inequality to find upper bound for $|(x^2-3)/(x-2)|$ if $x$ ranges over $|x-1| \lt \frac23$

I'm having trouble understanding the triangle inequality.

So far I have that $\frac13 \lt x \lt \frac53$

I just don't know how to apply that to find the bounds and my notes from class are unclear!